TY - JOUR
T1 - On the general asymptotic expansions of kυ-transforms
AU - Dai, H. H.
N1 - Publication information for this record has been verified with the author(s) concerned.
PY - 2007/5/10
Y1 - 2007/5/10
N2 - Theorems are established to obtain the general asymptotic expansions of the Kυ-transforms. It is shown that, under certain circumstances, the asymptotic expansion of Kυ-transform F(s) as s → 0+ or s → ∞ is obtained by integrating term by term the asymptotic expansion of the function at t → ∞ or t → 0+. In the case that the function has a power expansion, the treatment of this problem can be found in the existing literature (e.g. [4],[5]). In this paper we assume that the function has a general expansion form. Three examples, including the case that the function has an exponentially small behaviour at the origin, are discussed.
AB - Theorems are established to obtain the general asymptotic expansions of the Kυ-transforms. It is shown that, under certain circumstances, the asymptotic expansion of Kυ-transform F(s) as s → 0+ or s → ∞ is obtained by integrating term by term the asymptotic expansion of the function at t → ∞ or t → 0+. In the case that the function has a power expansion, the treatment of this problem can be found in the existing literature (e.g. [4],[5]). In this paper we assume that the function has a general expansion form. Three examples, including the case that the function has an exponentially small behaviour at the origin, are discussed.
KW - Asymptotic expansion
KW - Kυ-transform
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U2 - 10.1080/00036819208840118
DO - 10.1080/00036819208840118
M3 - 21_Publication in refereed journal
VL - 46
SP - 157
EP - 174
JO - Applicable Analysis
JF - Applicable Analysis
SN - 0003-6811
IS - 3-4
ER -